On orders of two transformation semigroups of the boolean

  • I.V. Livinsky Taras Shevchenko National University, 64/13 Volodymyrska str., 01601, Kyiv, Ukraine
  • T.G. Zhukovska Lesya Ukrainka East European National University, 13 Voli avenue, 43025, Lutsk, Ukraine
Keywords: semigroup, order-preserving transformation, order-decreasing transformation, monotone boolean functions
Published online: 2014-12-27


We consider the semigroup $\mathcal{O}(\mathcal{B}_n)$ of all order-preserving transformations $\varphi : \mathcal{B}_n \rightarrow \mathcal{B}_n$ of ordered by inclusion boolean $\mathcal{B}_n$ of $n$-element set (i.e. such transformations that $A \subseteq B$ implies $\varphi(A) \subseteq \varphi(B)$) and its subsemigroup $\mathcal{C}(\mathcal{B}_n)$ of those transformations for which $\varphi(A) \subseteq A$ for all $A \in \mathcal{B}_n$. Orders of these semigroups are calculated.
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How to Cite
Livinsky I., Zhukovska T. On Orders of Two Transformation Semigroups of the Boolean. Carpathian Math. Publ. 2014, 6 (2), 317-319.